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ISSN 1088-6850(e) ISSN 0002-9947(p)

Depth zero Boolean algebras

Author(s): Asher M. Kach
Journal: Trans. Amer. Math. Soc. 362 (2010), 4243-4265.
MSC (2000): Primary 03D45
Posted: March 23, 2010
MathSciNet review: 2608405
Retrieve article in: PDF

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Abstract: We study the class of depth zero Boolean algebras, both from a classical viewpoint and an effective viewpoint. In particular, we provide an algebraic characterization, constructing an explicit measure for each depth zero Boolean algebra and demonstrating there are no others, and an effective characterization, providing a necessary and sufficient condition for a depth zero Boolean algebra of rank at most $\omega$ to have a computable presentation.

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